Optimal bandwidth selection for local linear estimation of discontinuity in density

•A new bandwidth selection rule for estimating functions of the discontinuity in the density is proposed.•The rule selects different bandwidths for both sides of the discontinuity and yields smaller asymptotic MSE than currently popular methods.•A simulation study demonstrates the advantage of the proposed bandwidth selection rule.•An empirical example illustrates the practical usefulness of our bandwidth selection rule.

We derive an optimal bandwidth selection rule for estimating a function of two one-sided limits of the probability density function at two cut-off points by the local linear estimation method. Our rule follows Arai and Ichimura (2015, AI, hereafter)'s principle and selects two bandwidths simultaneously, one for each cut-off point. Simulation results are presented. We also illustrate the usefulness of the method in an empirical application.